*3.5. Control of EES, Charging and Discharging Characteristics*

Among energy storage devices, chemical batteries are increasingly used in professional power engineering [62]. The desirable features of batteries are their high energy density, high charge and discharge power and long life cycle. Other aspects are also relevant, such as the methods of determining the state of charge (SoC) and the possibilities of recycling [63]. For this reason, lithium-ion batteries are the most commonly used in battery energy storage (BES). The advantages of this type of battery include the fact that they have an energy density of 160 Wh/kg, a power density of up to 350 W/kg and a lifetime greater than 1000 charging and discharging cycles. The disadvantages of a lithium-ion battery include its high cost and the need for a heating and cooling system.

The main issue connected with controlling energy flow to and from an energy storage device is the correct determination of its operating characteristics [64]. Characteristics are defined by the manufacturer and they depend on the storage design. Furthermore, the system operator can control the storage operation using them. The rate of charging or discharging energy storage (also called C-rate) when using lithium-ion batteries can be determined as the value of the current at which the energy storage is discharged [65]. It is often expressed as the ratio of the battery capacity to the time of discharge. For example, a discharge rate of 1C means that storage will be completely discharged in 1 h. On the other hand, a discharge rate of 0.5C means that the same storage will be completely discharged in 2 h. [66] The storage charging or discharging rate is also determined by the remaining energy. The relative value of the remaining energy in relation to the rated capacity is called the state of charge (SoC) [67]. The characteristics of the dependence of the storage charging and discharging power on the SoC level should be provided by the manufacturer. The operator can change the shape of the characteristics within certain limits, for example, by preferring quick or slow charging or discharging in a specific SoC range [68]. In some cases, such shaping of characteristics can optimize storage efficiency and increase its lifetime and safety.

An important aspect of modeling energy storage operation is its lifetime and the decrease in capacity when using the battery. Reference [69] describes the impact of the ambient temperature and depth of discharge on the wear and tear and degradation cost of storage.

To ensure that each cell operates correctly within a certain voltage, temperature and current range during charging and discharging, the battery requires a built-in controller that communicates with the battery management system (BMS). The power value regulated by the BMS takes into account both the technical limitations of the technology and the safety conditions of the storage. The BMS is designed to maintain the efficient operation of the storage. The control is based on the current state of battery operation, that is, state of charge (SoC), temperature, counted discharge cycles and so forth.

The storage charging and discharging rate are especially affected by:


For the selected type of storage system, the dependence of charging and discharging power on the degree of SoC (modified Ragone plot) can be determined. The speed of charging (discharging) is determined by the power and is expressed in Watts or as a relative value in relation to the nominal power of the container. However, the SoC can also be defined as energy in Watt-hours or as a relative value in relation to the nominal capacity of the storage tank. Exemplary charging (discharging) of typical storage based on lithium-ion batteries is shown in Figure 3. An appropriate sign of the battery power was assumed for charging (positive-red) and discharging (negative-blue). The presented characteristics are typical for the lithium-ion batteries. Characteristics express the limitations of available power depending on the current SoC level. In discussed VPP, the storage unit has a power of 500 kW and is composed of lithium-ion batteries. It requires individual investigations to reveal the "real" charging/discharging characteristic, which may differ from that presented in Figure 3.

**Figure 3.** Dependence of charging and discharging power from the state of charge (SoC): Charging (positive-red) and discharging (negative-blue).
